Model & verification

Scope and provenance

This separate Studio combines editable neural-electrode layouts with a reduced single-metal polymer process. Version 2.0.0 was reconstructed from a surviving v1 project export, which contained six historical runs. The original source and reported 74-test suite were not recovered. Imported results are labeled historical and must be recomputed; v2 is not a byte-for-byte reconstruction of v1.

Geometry and process

Dimensions are micrometres in a 320 × 1000 window. Circles, elliptical sites, rings, rotated rectangles and round-ended polyline traces are rasterized at cell centres. The default grid is 2 µm; 1 µm permits refinement, while 4 µm deliberately exposes coarse-grid sensitivity. Material thickness remains continuous. Outline clipping occurs at stage 8; release changes the stage label without solving mechanics.

The stage selector represents carrier, base polymer, resist, development, deposition, lift-off, encapsulation, contact etch, outline and release. The view displays conductor and exposed-metal footprints, not a complete three-dimensional material stack. Ideal outline etching and an ideal metal etch stop are assumed. Base erosion, adhesion, chemistry, stress, stiction and lifetime are not calculated.

The educational lift-off margin is undercut − resist thickness × tan(deposition angle) − metal thickness. A nonpositive margin or resist no thicker than the metal blocks processing at lift-off. The blocked specimen uses a conservative blanket-conductor surrogate; its resistance is not reported. This threshold is an illustrative geometric criterion, not a calibrated fabrication recipe.

Contact etch depth is time × rate. Mask consumption is depth / selectivity. Once the mask is consumed, protected cap also etches. Openings expand laterally by depth × the lateral ratio, and are translated and rotated about (160, 494) µm. Exposure requires cleared cap over actual metal. Intact paths with covered site or pad are reported separately from accessible paths.

Electrical calculation

Four-neighbour flood fill determines metal connectivity; diagonal touching cells do not conduct. Shared conductive components flag shorts between terminal sets. Each isolated connected channel is solved as a square-cell sheet network with edge conductance t / ρ. The full site footprint is held at 1 V and the full pad at 0 V. All other conductive cells satisfy Kirchhoff’s current law. The resulting resistance is 1 V divided by terminal current.

A diagonally preconditioned conjugate-gradient solver uses a relative residual threshold of 10⁻⁹ (with an absolute floor of 10⁻⁹) and at most 4000 iterations. Unconverged, open, shorted or blocked results do not produce a resistance value. Ideal terminal footprints exclude spreading inside contacts and any contact resistance. This is metal-path resistance, not electrode–electrolyte impedance, tissue impedance, stimulation efficacy or recording quality.

Verification and numerical limits

Automated checks compare the network with an independent rectangular-resistor calculation, verify resistivity and thickness scaling, test breaks and bridges, underetch, mask exhaustion, misalignment, blocked lift-off, stage ordering, annular geometry, deterministic replay and bounded imports.

The 2 µm reference yields 13.664 Ω per channel, consistent with a 672 µm terminal-to-terminal path, a 12 µm trace and 0.2 µm metal at 4.88 × 10⁻⁸ Ω·m. The 1 µm result agrees within 0.5%. The 4 µm grid samples that same trace as 16 µm wide and yields 10.309 Ω: coarse-grid results must not be presented as converged. Arbitrary narrow or rotated geometries require their own refinement comparison.

Version 2 includes lateral etch expansion in exposed area; historical v1 area values may differ. No measured process dataset calibrates the illustrative rates or thresholds. A channel labeled accessible only meets geometric continuity, isolation, site exposure and pad exposure tests; unintended exposure must be inspected separately.

Files and reproducibility

Project JSON retains design, recipe, defects, grid and up to 40 run records. Version 1 imports retain historical provenance. Replay restores inputs and requires a new calculation. Browser saves remain local to this browser; exported JSON is the portable backup. SVG output is a raster conductor footprint for teaching, not a qualified fabrication mask.

Process references

EPFL CMi — Photoresist Selection describes how resist profiles, undercut and deposition direction affect lift-off. It also discusses etch selectivity. Those mechanisms motivate this teaching model; EPFL does not establish the simulator’s numerical threshold.

The separate Microfabrication Laboratory methods collects the underlying polymer-MEA process references and its own model limitations.